BrauerAlgebra

: the diagrams that are perfect matchings — every point paired with exactly one other. Dimension .

WikipediaBrauer algebra↗WikidataQ4958224↗

BrauerAlgebra(n)the Brauer algebra on strands

Domain: Diagram algebras

Details

• Dimension = 1, 3, 15, 105 — the perfect matchings of points
• Contains the symmetric group: a permutation diagram is a matching whose every block joins a top point to a bottom one
• The generators satisfy , the braid relation, and
• Restricting further to the PLANAR matchings gives TemperleyLiebAlgebra

Examples

See also: TemperleyLiebAlgebra, PartitionAlgebra, Diagram